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Efficiency and Equilibria in Games of Optimal Derivative Design

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  • Ulrich Horst
  • Santiago Moreno-Bromberg

Abstract

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal-agent models that are extended within, here the presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie-breaking rules. The main results of this paper are a proof of existence of (mixed-strategies) Nash equilibria in the case of profit-maximizing agencies, and of socially efficient allocations when the firms are risk minimizers. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix-mix" tie-breaking rule, in which case firms share the whole market over given proportions.

Suggested Citation

  • Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2010-035
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    Cited by:

    1. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    4. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    5. Michail Anthropelos, 2012. "The Effect of Market Power on Risk-Sharing," Papers 1206.0384, arXiv.org, revised May 2016.
    6. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Alexander L. Baranovski, 2010. "Dynamical systems forced by shot noise as a new paradigm in the interest rate modeling," SFB 649 Discussion Papers SFB649DP2010-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Jana Bielagk & Ulrich Horst & Santiago Moreno--Bromberg, 2016. "A Principal-Agent Model of Trading Under Market Impact -Crossing networks interacting with dealer markets-," Papers 1607.04047, arXiv.org, revised Aug 2016.
    13. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Adverse selection; Nash equilibria; Pareto optimality; risk transfer; socially efficient allocations; tie-breaking rules;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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